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By utilizing known characterizations of w-Noetherian rings in terms of injective modules, we give more characterizations of w-Noetherian rings. More precisely, we show that a commutative ring R is w-Noetherian if and only if the direct limit of GV-torsion-free injective R-modules is injective; if and only if every R-module has a GV-torsion-free injective (pre)cover; if and only if the direct sum of injective envelopes of w-simple R-modules is injective; if and only if the essential extension of the direct sum of GV-torsion-free injective R-modules is the direct sum of GV-torsion-free injective R-modules; if and only if every Fw,f(R)-injective w-module is injective; if and only if every GV-torsion-free R-module admits an i-decomposition.
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참고문헌 (26)
참고문헌 신청
C. Faith / 1967 / Direct sum representations of injective modules / J. Algebra 5 : 203 ~ 221
E. Enochs / 2000 / Relative Homological Algebra / Walter de Gruyter
E. Matlis / 1958 / Injective modules over Noetherian rings / Pacific. J. Math 6 : 512 ~ 528
F. Wang / 1997 / On w-modules over strong Mori domains / Comm. Al- gebra 25 (4) : 1285 ~ 1306
F. Wang / 1999 / On strong Mori domains / J. Pure Appl. Algebra 135 (2) : 155 ~ 165
E. Enochs / 2000 / Relative Homological Algebra / Walter de Gruyter
E. Matlis / 1958 / Injective modules over Noetherian rings / Pacific. J. Math 6 : 512 ~ 528
F. Wang / 1997 / On w-modules over strong Mori domains / Comm. Al- gebra 25 (4) : 1285 ~ 1306
F. Wang / 1999 / On strong Mori domains / J. Pure Appl. Algebra 135 (2) : 155 ~ 165
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